Hoping to recover from a sobering 3-0 defeat to Arsenal in the Community Shield, City made a purposeful start here, coming close early on as Phil Foden’s neat flick found Rico Lewis, who was thwarted at close range by Djorde Petrovic.
And City were knocking at the door again when Nico O'Reilly’s lung-busting run ended with a ball across goal that couldn’t be turned goalwards by Erling Haaland.
At the other end, Rayan forced a save from Gianluigi Donnarumma at his near post, easing in a positive period that led to the opening goal, as Rayan slipped in Evanilson, whose first-time ball across goal was side-footed home by the arriving Marcus Tavernier.
Maresca’s side had dominated possession, but aside from a well-saved Haaland header, barely threatened an equaliser before the break.
Instead, it was Bournemouth looking the likelier to score next, Tavernier bending an effort just wide before Justin Kluivert’s low shot was parried away by Donnarumma.
Bournemouth had won just two of their nine PL openers (D3, L4), but luck appeared to be on their side as they survived a major scare after the restart, seeing Marc Guehi miss a free header from inside the six-yard box with the goal at his mercy.
Maresca turned to his bench for inspiration, and there were moments of promise as Haaland peppered the Bournemouth goal, yet the new-look striker continually failed to make clean contact.
Thankfully for the home fans, Guehi atoned for his earlier miss with a bullet header that arrowed into the net six minutes from time, having been left completely unmarked again.
That set up an intriguing finale, and there was still time for Gvardiol to turn the game on its head in stoppage time, surviving a VAR check by staying onside to tuck home at the death.
Despite a commendable performance, defeat for Rose means that a new manager has yet to win at the Etihad Stadium in their first PL game (D1, L4).
That dramatic late goal ends the Cherries’ unbeaten league run of 18 matches (W8, D10). As for City, a late turnaround won’t mask an underwhelming performance but does at least give Maresca a winning start in the league.
Flashscore Man of the Match: Marc Guehi (Manchester City)